The number of teams and matches in the soccer league illustrates permutation and combination
There are 12 teams in the soccer league in the first season
How to determine the number of teamsThe number of teams in the soccer league is given as n.
So, the total number of matches played in a season is:
Matches = n(n-1)/2
When the number of teams increases by 2, we have:
Matches = (n + 2)(n + 2 -1)/2
Also, the number of matches increases by 27.5%.
So, we have:
Matches = n(n-1)/2 * (1 + 27.5%)
Equate both equations
[tex]\frac{(n + 2)(n + 2 -1)}{2} = \frac{n(n-1)}{2} * (1 + 27.5\%)[/tex]
Simplify
[tex]\frac{(n + 2)(n + 1)}{2} = \frac{n(n-1)}{2} * (1.275)[/tex]
Multiply through by 2
[tex](n + 2)(n + 1) = n(n-1) * (1.275)[/tex]
Expand
[tex]n^2 + 3n + 2 = 1.275n^2 - 1.275[/tex]
Collect like terms
[tex]n^2 -1.275n^2+ 3n + 2 +1.275 = 0[/tex]
Evaluate the like terms
[tex]-0.275n^2+ 3n + 3.275 = 0[/tex]
Using a graphing calculator, we have:
n = -1 or n = 11.909
n cannot be negative.
So, we have:
n = 11.909
Approximate
n = 12
Hence, there are 12 teams in the soccer league in the first season
Read more about permutation and combination at:
https://brainly.com/question/12468032
If x = –12 and y = 16, evaluate x + y – 5x.
Answer:
64
Step-by-step explanation:
- 12 + 16 - 5 (-12)
- 12 + 16 + 60
4 + 60
= 64
Answer:
64
Step-by-step explanation:
If x = –12 and y = 16, evaluate x + y – 5x.
Solution,
= x + y - 5x
= -12 + 16 - 5 ( -12 )
= - 12 + 16 + 60
= - 12 + 76
= 64
Look at the picture to answer.
Find the volume of the composite figure. Round the answer to the nearest tenth.
Volume = ____cm3
Answer:
around 433.1 cm
find the first shape's volume.
L x W x H method.
[tex]4 * 10 * 8 = 320cm[/tex]
Length is eight, height is 4, and width is 10.
Now, the 2nd shape.
The formula of finding a sphere with a radius of 3 is V = 4/3[tex]pi^3[/tex]
In that case, the answer should be an estimated 113.1
Add the two cm's together.
[tex]320 + 113.1 = 433.1[/tex]
Please note that this is rounded to tenths place and estimated.
Please mark brainliest. Thanks! :)
First of all we will divide the figure in two shapes. One is hemisphere and other is a cuboid.
Volume of hemisphere:
[tex] \boxed{ \tt \:v = \frac{2}{3} \pi {r}^{3} }[/tex]
Volume of cuboid:
[tex] \boxed{ \tt \: v = length \times breadth \times height}[/tex]
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Volume of the hemisphere ⤵️r = 3 pi = 22/7[tex] \sf \dashrightarrow \: v = \frac{2}{3} \times \frac{22}{7} \times {3}^{3} [/tex]
[tex] \sf \dashrightarrow \: v = \frac{2}{ \cancel3} \times \frac{22}{7} \times \cancel{27}[/tex]
[tex] \sf \dashrightarrow \: v = 2 \times \frac{22}{7} \times 9[/tex]
[tex] \sf \dashrightarrow \: v = \frac{396}{7} [/tex]
[tex] \sf \dashrightarrow \: v = 56.6 \: {cm}^{3} [/tex]
Volume of the cuboid ⤵️Length = 8cmBreadth = 10cmHeight = 4cm[tex] \bf \multimap \: v = 8 \times 10 \times 4[/tex]
[tex] \bf \multimap \: v = 80 \times 4[/tex]
[tex] \bf \multimap \: v = 320 \: {cm}^{3} [/tex]
Now, Total volume ↯[tex] \rm \leadsto \: total \: volume = 56.6 + 320 \: {cm}^{3} [/tex]
[tex] \rm \leadsto \: total \: volume = 376.6\: {cm}^{3} [/tex]
If we round to the nearest tenth the total volume is ᭄
[tex] \rm \twoheadrightarrow volume = 380 \: {cm}^{3} [/tex]
A costume closet contains 8 dresses, 3 shirts, 5 pairs of pants, and 4 hats. What is the probability of randomly selecting a hat from the costume closet?
A.3/20
B.1/5
C.1/4
D.2/5
The probability of randomly selecting a hat from a costume closet of 8 dresses, 3 shirt , 5 pairs of pant and 4 hats is 1 / 5
What is probability?probability = number of favourable outcomes / total number of the possible outcome
Therefore,
probability of randomly selecting a hat = number of hat / total number of possible outcome
Therefore,
number of hat = 4
total number of possible outcome = 8 + 3 + 5 + 4 = 20
Therefore,
probability of randomly selecting a hat = 4 / 20
probability of randomly selecting a hat = 1 / 5
learn more on probability here: https://brainly.com/question/26285302
PLEASE YALL I NEED TO GET THIS DONE TN
Ricky is playing a game using 5 cards and a spinner. The cards are numbered 1,2,3,4, and
5 and the spinner is divided into three equal parts. If Ricky picks a card and spins the
spinner, what number would represent the sample size?
options
15
8
3
5
Answer:
15
Step-by-step explanation:
The cards have 5 possible outcomes and the spinner has 3 possible outcomes. To find the sample size, you need to calculate the number of possibilities when drawing 1 card and landing on 1 side of the spinner. You can do this by multiplying the possible outcomes together.
5×3 = 15
Therefore, the sample size is 15.
Answer:
Option 1: 15
Step-by-step explanation:
Ricky is playing a game using 5 cards and a spinner
Card 1 , Card 2 , Card 3 , Card 4 , Card 5
and
㉦ Green, Red, Blue
Ricky picks a card and spins the spinner
The sample size outcome is:
{(1, G) (1, R) (1, B) (2, G) (2, R) (2, B) (3, G) (3, R) (3, B) (4, G) (4, R) (4, B) (5, G) (5, R) (5, B)}
Sample size is 15
Please Help me !!! Please Help .......Carla was asked to draw all the lines of symmetry for a regular pentagon. She drew the picture below. What was Carla's mistake?
Answer:
There should be 5 lines of symmetry.
Step-by-step explanation:
Carla's draw only one line of symmetry but in a regular pentagon there should be 5 line of symmetry.
Here,
Carla was asked to draw all the lines of symmetry for a regular pentagon.
She drew the picture as shown.
We have to find Carla's mistake.
What is Regular Pentagon?
A regular pentagon is a pentagon that has 5 equal sides and 5 equal angles.
Now,
As shown in figure,
Carla's draw only one line of symmetry.
But in a regular pentagon there should be 5 line of symmetry.
Hence, There should be 5 line of symmetry.
Option 4 is true.
Learn more about the regular pentagon visit:
https://brainly.in/question/268970
#SPJ6
Write and equation to represent the function.
Input(x). 1. 2. 3. 4
Output(y). 6. 10. 14. 18
Answer:
in explanation
Step-by-step explanation:
Input to output so for the input when it is 1=6 because it starts at 5 and then 8 what I mean is when the input comes out the output is going to be 3 more greater than last time.
So 1=6 so 6 is 5 more then
2 to 10=8 so 5 more went to 8 more.
Next is 3 and 14 so 3 more again because 8 + 3=11 so in that case that next number is 4 it will be 14 more
So 14 more than 4=18 and that is the output.
Also for the output it adds 4 for the numbers 6 + 4=10 + 4=14+ another 4=18.
And input is just plus 1.
Hope it helps have a great day:)
Solve for v.
-4 + v = -9
v =
Answer:
v = -5
Step-by-step explanation:
Add 4 on both sides.
-9 + 4 = -5
v = -5
PLEASE HELP ASAP I WILL MARK BRAINLIEST
Answer:
A
Step-by-step explanation:
Answer:
r ≈ 12.1
Step-by-step explanation:
from the diagram the radius r of the circle is GM and GE and
GA = r - 4
using Pythagoras' identity in right triangle AGM , then
9² + (r - 4)² = r² ← expand factor on left using FOIL
81 + r² - 8r + 16 = r² ( subtract r² from both sides )
97 - 8r = 0 ( subtract 97 from both sides )
- 8r = - 97 ( divide both sides by - 8 )
r = [tex]\frac{-97}{-8}[/tex] ≈ 12.1 ( to 1 dec. place )
If you were to solve this inequality,
do you need to flip the Inequality symbol?
Answer:
YES
Step-by-step explanation:
To solve this inequality, you need to multiply both sides by -5.
When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.
Answer: YES
Is (5+4x^0)2x a monomial? What about (5+4x²)2x? Please explain why.
Answer:
Neither are monomials.
Step-by-step explanation:
Take a look at the root word of monomials.
Mono = One In both of these expressions, there is more than one term. For them to considered or classified as monomials, they have to have one terms. Therefore, neither of these are monomials but instead are trinomials which have three terms.Neena a has $25.00 in nickels. How many nickels does Neena have?
A: 5
B: 125
C: 250
D: 500
Answer:
The answer would be D
Step-by-step explanation:
Because We multiplied 25 by 100, because there are 100 cents in a dollar, and we divided 2,500 by 5, because there are 5 cents in a nickel.
helppppppppppppppppppppppp
Hey there!
In order to simplify the first expression, we need to use the Distributive Property:
4(7x-4)=28x-16 (the same as 4*7x-4*4)
Hence, the equivalent expressions are
[tex]\boxed{\boxed{\bold{28x-16\;and\;4*7x-4*4}}}[/tex]
[tex]\rule{200}{2}[/tex]
In order to simplify the second expression, we need to combine like terms:
11y+3y+9y
11y+12y ✓
23y ✓
Hence, the equivalent expressions are
[tex]\boxed{\boxed{\bold{11y+12y\;and\;23y}}}[/tex]
Hope everything is clear.
Let me know if you have any questions; if so, please comment.
#LearningDoesn'tEnd
#LearningIsFun
How does national glory increase?
Find the values of the missing arc
Show step by step !
Answer:
arc QS = 95°
Step-by-step explanation:
the inscribed angle QSR is half the measure of its intercepted arc RQ , then
arc RQ = 2 × 95° = 190°
the sum of the arcs in a circle = 360° , then
arc QS = 360° - arc SR - arc RQ = 360° - 75° - 190° = 95°
Jenny had $2.40 deducted from her monthly allowance every time she forgets to do a chore. If she forgets three times in one month, what will be the change in Jenny's total allowance?
Answer:
-$7.20
Step-by-step explanation:
-$2.40 x 3 = -$7.20
How many more miles is 8 2/3 from 5 1/2
Answer:
3.167
Step-by-step explanation:
subtract 5 1/2 from 8 2/3
Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of a equilateral triangle?
Answer:
(B)45°, 67.5°
Step-by-step explanation:
A regular polygon is a polygon in which all the sides are equal.
An Octagon is a polygon with 8 sides.
Since it is a Regular polygon, the following holds:
1.The Radii are equal
2. The angle Subtended by two radii are equal for all triangles in the octagon.
3. There are 8 Isosceles triangles in the octagon.
(a)Measures of angle formed by Two radii
From the centre of the octagon, there are 8 equal angles.
Sum of Angle at a point= 360°
Each Angle=360°÷ 8 = 45°
The measures of angle formed by two radii is 45°.
(b)a radius and a side of the polygon.
Since the triangles are Isosceles, the base angles at the side of the octagon are equal.
Let x be the angle made by a radius with a side.
From (a) above,
x+x+45°=180°(Sum of Angle in a Triangle)
2x=180-45°
2x=135°
x=135°÷2=67.5°
The angle between a radius and a side of the polygon is 67.5°.
Step-by-step explanation:
Find all whole values for y for which the double inequality is true: −5
Answer:
0, 1
Step-by-step explanation:
Whole numbers do not include negatives !
Based on the y-values in the table, the exponential function appears to grow
then linear function.
Answer:
what is the question exactly
Step-by-step explanation:
Answer:
(Its so important to show pictures where pictures when they are needed lol)
Based on the y-values in the table, the exponential function appears to grow FASTER THAN then linear function.
Step-by-step explanation:
Picture below
Identify this sequence: 12,19,26,33,40,47. The next term is___??
Answer:
54
Step-by-step explanation:
does anybody know how
Answer:
30
Step-by-step explanation:
5z + 20 + 10 - 5z
= 5z - 5z+ 20 + 10
= 30
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP
Answer:
(0,6)
Step-by-step explanation:
First, deal with the reflection. Reflecting the triangle over the x axis will reflect it vertically into the upper right quadrant. Because it is reflected vertically, the x values of the vertices will not change and the y values will be the negative of whatever value they are originally. If the coordinates of each vertex are (x,y), you can easily find their new location by changing it to (x,-y). After the reflection, the coordinates of the vertices are as follows:
A = (2,6) [originally (2,-6)]
B = (2,1) [originally (2,-1)]
C = (5,6) [originally (5,-6)]
Now, deal with the translation. A translation of -5 units horizontally means that the triangle will be moving 5 units to the left. The y values will be unaffected by the translation. To find the new coordinates, subtract 5 from the x values of the coordinates after the reflection.
A = (-3,6)
B = (-3,1)
C = (0,6)
Therefore, the answer is (0,6).
f - 20 = -34.75
6
This is f/6 like a fraction.
Answer:
f/6 - 20 = 34.75
f = -88.5
Step-by-step explanation:
-88.5/6 = -14.75
-14.75 - 20 = 34.75
a group of students there any Circle to play a game the circle has a diameter of 22. which measurement is close to the circumference of the circle in meters?.
Hello! The answer is 69.11
Step-by-step explanation:
This is the formula you use: Circumference = 2 * π * r
r = Radius, the radius is just half of the (22) diameter, so half of 22 is 11.
2 * π * 11 = 69.11
What's the answer to -12÷(-3)
Answer:
4
Step-by-step explanation:
(-12) ÷ ( -3) = 4
In multiplication and division, if number of negative sign is even, the the result will be a positive integer
Greg has a credit card which requires a minimum monthly payment of 2.06% of the total balance. his card has an apr of 11.45%, compounded monthly. at the beginning of may, greg had a balance of $318.97 on his credit card. the following table shows his credit card purchases over the next few months. month cost ($) may 46.96 may 33.51 may 26.99 june 97.24 june 112.57 july 72.45 july 41.14 july 101.84 if greg makes only the minimum monthly payment in may, june, and july, what will his total balance be after he makes the monthly payment for july? (assume that interest is compounded before the monthly payment is made, and that the monthly payment is applied at the end of the month. round all dollar values to the nearest cent.) a. $812.86 b. $830.31 c. $864.99 d. $1,039.72
The total balance of Greg account after he makes the monthly payment for July is $864.99.
What is monthly payment?Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.
It can be calculated with the following formula.
[tex]M=P\left(1-\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]
Here, (P) is the principal amount, (r) is the interest rate and (t) is time.
Greg has a credit card which requires a minimum monthly payment of 2.06% of the total balance.
His card has an apr of 11.45%, compounded monthly. At the beginning of May, Greg had a balance of $318.97 on his credit card.
In the Month of May he make payment of 46.96, 33.51, and 26.99. Greg had a balance of $318.97 on his credit card. The total balance after the end of may is,
[tex]P=46.96+33.51+26.99+318.97\\P=426.43[/tex]
The financial charge on this payment with Apr 11.45% is 4.07. Thus, the payment become 430.5.
The payment for the June 97.24, 112.57,72.45. The payment at the end of June is 719.56 and financial charge is 10.22.
The payment become 722.98. The payment for the June 41.14, 101.84. At the end of July 865.96.
The total balance of Greg account after he makes the monthly payment for July is $864.99.
Learn more about the monthly payment here;
https://brainly.com/question/2151013
Answer:
b
Step-by-step explanation:
What is the volume of the prism?
in.3.
Answer:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Step-by-step explanation:
..
Please help very urgent!!
Answer:
4300 [tex]\frac{67}{1000}[/tex]
Step-by-step explanation:
evaluate each part
4 × 1000 = 4000
3 × 100 = 300
6 ×[tex]\frac{1}{100}[/tex] = [tex]\frac{6}{100}[/tex] × [tex]\frac{10}{10}[/tex] = [tex]\frac{60}{1000}[/tex]
7 × [tex]\frac{1}{1000}[/tex] = [tex]\frac{7}{1000}[/tex]
Thus
4000 + 300 + [tex]\frac{60}{1000}[/tex] + [tex]\frac{7}{1000}[/tex]
= 4300 [tex]\frac{67}{1000}[/tex]
Expand it please
(3h+7k)2
Answer:
6h+14k
Step-by-step explanation:
Multiply 2by 3h which gives 6h then multiply 7k by 2 which gives 14k.
Since 6h and 14k are not like terms u cannot add so your answer will be 6h + 14k.
Answer:
9h² + 42hk + 49k²
Step-by-step explanation:
Given
(3h + 7k)²
= (3h + 7k)(3h + 7k)
Each term in the second factor is multiplied by each term in the first factor, that is
3h(3h + 7k) + 7k(3h + 7k) ← distribute both parenthesis
= 9h² + 21hk + 21hk + 49k² ← collect like terms
= 9h² + 42hk + 49k²
If you have 15 pieces of candy and you gave 6 of them away, how many pieces of candy do you have left?
Only for Elementary students to answer. Thank You
Answer:
56
Step-by-step explanation: